Linear_Regression_Python.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Linear Regression Python.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/kaustubholpadkar/Linear_Regression-Gradient_Descent-Octave/blob/master/Linear_Regression_Python.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "ON4WbEBvk9Z9",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Linear Regression\n",
        "## Predicting Student's marks from Study Hours"
      ]
    },
    {
      "metadata": {
        "id": "RKxoZ5lknWll",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Import Libraries"
      ]
    },
    {
      "metadata": {
        "id": "Lq6qDjhHnbak",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "W5b_-H-zn3_O",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Read Data"
      ]
    },
    {
      "metadata": {
        "id": "T1a23JYWn5oM",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "data = np.genfromtxt('https://github.com/raw/kaustubholpadkar/Linear_Regression-Gradient_Descent-Octave/master/data.csv', delimiter=',')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Ip2EQ_PGoQJO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "226bbb0b-0845-46c3-9561-d7fcfb27eb1e"
      },
      "cell_type": "code",
      "source": [
        "data.shape"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "metadata": {
        "id": "8rMv-L53odN5",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Seperate Data into X and Y"
      ]
    },
    {
      "metadata": {
        "id": "uop_AFQSolHl",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "X = data[:, 0]\n",
        "Y = data[:, 1]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "wPSTKDAXpLAN",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Visualize the Data"
      ]
    },
    {
      "metadata": {
        "id": "qdTK7EOQpL5Y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "outputId": "251e0c8c-2186-411a-df29-502c90b4cc85"
      },
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "plt.scatter(X, Y)\n",
        "fig.suptitle('Student Data : Expected Marks vs Hours of Study', fontsize=18)\n",
        "plt.xlabel('Hours of Study', fontsize=14)\n",
        "plt.ylabel('Expected Marks', fontsize=14)\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SIDUG9hJ4eHggIiICERERmDBhAgYNGoRdu3Zh3rx5cHd3N+pcz9+8iguy+vZ17dq1yI9f\no3r16jqvNc2ilnDt2jUAQJ06dQAAS5cuxddff41u3bph6tSp8PX1hbOzM2bMmIHHjx8Xe67SvNdY\nAQEBeOWVV0Qff+vWLTg5OeHOnTvIysoqEsT15bnm7/j8vhEjRmib6wvz9/fXFgBMbdot6fyaAqU+\nxhb8nJ2d0a1bN2zbtg3z58/H3r17UbNmTYN9j9OnT8fRo0cxZMgQREVFoVy5cnByctJ2GxVm6AZ+\n7do1bRN8q1atdG6yVatWxa5du3D58mUcO3YMJ0+exKJFi7B+/Xps27ZNb4EGAF544QXUq1cPhw8f\nxogRI3Dy5Ek8fvxYp5Bi6rk1KleubPCae77VATD8G9Z3TRV3XGHPdyUCpn+n0qavJC4uLggNDUVo\naChGjRqF+fPnY/v27drWS2MUzgtDeVNQUKDz2snJCb169UJMTAxu374NpVKJa9eu4cMPPzTuy1gB\nA/tz8vLy8Ntvv6Fs2bJ6S3QeHh5o1aoVrl+/jtTUVIO1SCcnpyLN9fn5+UhPT9e+1pSc9Q3Qe75Z\n0sfHB0qlErm5uUYFIkvIycnBvn37EBwcrB3NumfPHgQGBmpnDmhkZmZCoVAUe77SvFdKu3fvxokT\nJ7By5Uq8++67WLp0KRYvXqxzzKNHj5CXl6dzg9Y0HVaoUEHb/KxWq4v9O2qaNgs3TQuCgEePHkGp\nVEKpVBp8X0nnF3vdidWzZ09s2LABx48fx6FDhzBixAi9x2VlZeGnn35C27ZttQM5gacD1J5vmRFj\n+/btUKlU6NWrF2bNmoUNGzYUCSRhYWEICwvDW2+9hTNnzmD48OH47rvvMGnSJIPn7dq1Kz766COk\npKTg4MGDqFatmt4pWqac21iVK1fWztB5nqZlRlOY0Xzv/Px8neuiuAKcPsZ+J7HpE+v3339HUlKS\n3tkUTk5O6NChA7Zv365tcdJHbF74+Pjovf7v3btXZFuvXr2wcuVK/PDDD1AqlShTpozegaG2hn3s\nhUybNg2zZs3SW0N88uQJLly4gPLlyxf5YanVau1x5cqVw/3793VKgCdOnNB5/cILL8Db2xu//PKL\nzmfExcVpfxzA05Jr06ZN8csvvxTpY9q5cye++OILo2tamjQXLqEaQ61WY968eUhJScFbb72l3f7k\nyRNUrlxZ59iDBw/i/v37OnmkLw1i32tJycnJWLJkCfr374+oqChMnz4d27dvx6lTp3SOU6vVRUZ2\nnzp1Cp6enggICEClSpVQs2ZNHDp0qMhYh3Xr1mHr1q0Angbel156CceOHdMpHJ47dw6NGzfGkSNH\nABS97sSeX+x1J1adOnUQGBiI1atXIzMz02AzvFqthiAIRf6+mzdvxpMnT4z6+1auXBkvvvgi5syZ\ng9OnT2Pjxo0AnnYLvffee0VWh2zWrBk8PT11Ctb6dOnSBQBw7NgxHD9+HN26ddPmc2nPbayIiAj8\n/vvvRYLNTz/9BIVCgWbNmgF41gX2/HFJSUnalrTilOY7iU2fWKtWrcKkSZMQHx+vd79mHIdmsK6+\n+4fYvAgJCcGVK1eQmZmp3Zabm4szZ84U+dzq1aujcePGOHToEPbv34+oqChR3S7Wxhr7c9zc3DB/\n/nxMnz4d/fr1w5AhQ7TT3+7evYvt27fj8uXLWLJkibZJS9NUtWbNGgQGBiIqKgqtW7fGF198gQ8+\n+AAdO3bEf//7X2zZskWnyVyhUKB///5Yt24d3nvvPXTq1AkPHjzAqlWr8NJLL+nUYiZPnozo6GgM\nGzYMU6dORbly5XDu3Dl8+eWX6N+/v9HNXpo0f//998jMzETz5s2LnSaWmJio/XHk5eUhPj4e3377\nLW7cuIE5c+boNI01adIEJ0+exPbt21GjRg2cPXsWsbGx6NixI44cOYKjR4+icePGetMg9r2aH/Dz\n7t+/j+joaAwcOBBvvvlmiXnwzz//FHvzCwgIQPny5bFgwQK4uLhoR8H27dsXu3fvxty5c7Fv3z5t\nk7y3tzc+//xzpKWl4eWXX8aRI0dw8eJFjB49WnutTJs2DRMnTsSIESMwduxYuLq64ujRo9i0aRNm\nzJih/eypU6dq/xs2bBhSUlLw2WefoXbt2tqRu/quOzHnN+a6E6t79+749NNPERYWpnceMvD0phsU\nFIQDBw6gcePG8Pf3x+HDh/HXX38hPDwcN2/exOnTp3UWhSpJv379cPz4cXz22Wdo3rw56tSpg6tX\nr+Lnn3/GhAkTUKNGDahUKuzbtw+PHz9Gx44diz1fpUqV0LBhQ6xZswaPHj3SKaSUK1euVOc21ptv\nvokDBw5g/PjxGDduHMqVK4ezZ8/i+++/x9ChQ7UVi9atW2Pjxo14//33MXbsWGRnZ+OLL75A3bp1\ncenSpWI/ozTfSWz6xJo2bRquXr2KwYMHY+jQoWjYsCHc3d2RmpqKw4cPY8+ePejXr5+2m0ff/UNs\nXgwaNAjHjh3DhAkT8MYbb+DJkydYt24dKlasqLcm37t3b8yePRsAdH6nNk2gIi5fviy89dZbQps2\nbYTg4GAhODhYaNOmjfD2228LV65c0Tn27t27Qo8ePYS6desKvXv3FgRBELKysoQ5c+YIERERQlhY\nmPD6668Lt2/fFnr06CEMGTJE+968vDzhgw8+EJo3by6EhIQIvXr1En755Rdh0qRJQkREhM7nXLly\nRRg1apTQoEEDITg4WOjYsaOwceNGQa1Wa4+ZOXOmEBgYKOTm5uq8t/D2/Px8Ydy4cUJISIjQtGlT\n4c6dO3rz4ezZs0JgYKDOf6+88orQsmVLYdq0acLvv/9e5D33798XxowZIzRo0EBo0qSJ8PbbbwvJ\nycnCxYsXhRYtWggNGjQQfvvtN71pEPtefe7cuSMEBgYKH3/8saE/qyAIgrBz584i30nff7t37xb2\n798vBAYGCvv379c5x61bt4Tg4GBh7ty5giAIwpAhQ4SIiAjhjz/+EAYPHiyEhoYKTZs2Ff71r38J\nKpVK570///yzEB0dLYSFhQkhISFCz549hf/85z9F0nno0CGhd+/eQr169YSGDRsK77zzjpCcnKzd\nr++6E3t+Y647Q/n3/DWTmJgo1KlTR/jmm290jm3btq0wc+ZMnXwbMmSIEBYWJkRERAjz588XsrKy\nhCNHjghNmjQRmjRpIty9e7fE6/h5qampQmRkpNC5c2chJydHSEtLE+bNmye0atVKCA4OFpo1ayYM\nHjxYOHbsWLHfS2Pr1q1CYGCg0L179yL7TD235ne0detWg8e0bdtW6Nevn862W7duCWPHjhUaNWok\nBAcHC507dxY2bNggFBQU6By3du1aoV27dkK9evWE7t27C7GxscL777+vk1crVqwQAgMDhfj4eLN8\nJ7Hp0/wuV6xYUeL5EhMThcWLFwudO3cWQkNDhVdeeUVo1qyZMHLkSOGHH37QOdbQPUxMXgiCIGzf\nvl1o3769EBwcLLRr107YuHGjsGnTJr15lJWVJYSFhQmRkZHCkydPSvwetsBJECQYKk3kQIYOHYq/\n/vqrSPM8Edm/vLw8tG7dGn379sW0adOsnRxR2MdORERkwLZt2/Do0SOdRXxsHfvYiYiICrly5Qou\nX76MTz/9FKNGjSqyKJUtY2AnIiIqZPDgwXB1dcXgwYMxefJkayfHKOxjJyIikhH2sRMREckIAzsR\nEZGMMLATERHJCAM7ERGRjDCwExERyQgDOxERkYwwsBMREckIAzsREZGMMLATERHJCAM7ERGRjDCw\nExERyQgDOxERkYwwsBMREckIAzsREZGMMLATERHJCAM7ERGRjDCwExERyQgDOxERkYwwsBMREckI\nAzsREZGMMLATERHJiIu1E2AOycmPrJ0Eq/Lx8UB6era1kyF7zGfLYD5Lj3lsGVLms5+fl8F9rLHL\ngIuLwtpJcAjMZ8tgPkuPeWwZ1spnBnYiIiIZYWAnIiKSEQZ2IiIiGWFgJyIikhGLBvabN28iKioK\nmzdvBgAkJiZi+PDhGDJkCIYPH47k5GQAwN69e9GnTx/069cP33//vSWTSEREZNcsFtizs7OxePFi\nNG/eXLtt+fLl6N+/PzZv3oz27dtj48aNyM7OxqpVq/Dvf/8bmzZtwtdff42MjAxLJZOIiMiuWSyw\nu7m5Ye3atfD399due++999CxY0cAgI+PDzIyMnDlyhXUq1cPXl5ecHd3R4MGDXDx4kVLJZOIiMiu\nWWyBGhcXF7i46H6ch4cHAECtVmPr1q2YMGECUlJSUKFCBe0xFSpU0DbRG+Lj4+Hw8zKLW6yAzIf5\nbBnMZ+nZcx7n5j1BeqYKPt5KuLvZ9jpr1shnq+eIWq3GjBkz0KxZMzRv3hz79u3T2S8IQonncPQV\nlPz8vBx+9T1LYD5bBvNZevaax+qCAmyLjcelm8lIy1ShgrcS4YF+GNCuFhTOtjcWXMp8tumV52bP\nno0XX3wREydOBAD4+/sjJSVFuz8pKUmn+Z6IiBzTtth4HL1wF6mZKggAUjNVOHrhLrbFxls7aTbF\nqoF97969cHV1xeTJk7Xb6tevj2vXriEzMxOPHz/GxYsX0ahRIyumkoiIrE2Vr8alm/q7ZS/dTIEq\nX23hFNkuizXFx8XFYenSpUhISICLiwsOHTqE1NRUKJVKDB06FABQs2ZNLFiwANOmTcOoUaPg5OSE\nCRMmwMvLfvuCiIio9B5mqZCWqdK7L/1RLh5mqeDv42HhVNkmiwX2kJAQbNq0SdSxnTp1QqdOnSRO\nERER2YtynkpU8FYiVU9w9/FyRzlPpRVSZZus3sdORERUEqWrAuGBfnr3hQdWhNLVsWdGPc/qo+KJ\niIjEGNCuFoCnferpj3Lh4+WO8MCK2u30FAM7ERHZBYWzM6KjAtGndU08zFKhnKeSNXU9GNiJiMiu\nKF0VHChXDPaxExERyQgDOxERSUKVr0ZSejbnmFsYm+KJiMis7G3pV7FU+Wq76NtnYCciIrPSLP2q\noVn6FQCiowKtlSyT2VtBxfZSREREdkuOS7/a2xr1DOxERGQ2YpZ+tSf2WFBhYCciIrPRLP2qjz0u\n/WqPBRUGdiIiMhu5Lf1qjwUVBnYiIjKrAe1qIapRdfh6u8PZCfD1dkdUo+p2ufSrPRZUOCqeiIjM\nSm5Lv9rbGvUM7EREJAm5LP1qbwUVBnYiIiIR7KWgwj52IiIiGWFgJyIikhEGdiIiIhlhYCciIpIR\nBnYiIiIZYWAnIiKSEQZ2IiIiGWFgJyIikhEGdiIiIhlhYCciIpIRBnYiIiIZYWAnIiKSEQZ2IiIi\nGWFgJyIikhEGdiIiIhlhYCciIpIRBnYiIiIZYWAnIiKSEQZ2IiIiGWFgJyIikhEGdiIiIhlhYCci\nIpIRBnYiIiIZYWAnIiKSkCpfjaT0bKjy1Rb5PBeLfAoREZGDUasLsPXoTVy6mYy0TBUqeCsRHuiH\nAe1qQeEsXb2agZ2IiEgCG/b9jqMX7mpfp2aqtK+jowIl+1w2xRMREZmZKl+Ns3GJevddupkiabM8\nAzsREZGZPcxSITkjR+++9Ee5eJilkuyzGdiJiIjMrJynEn7ly+jd5+PljnKeSsk+m4GdiIjIzJSu\nCjQLqaJ3X3hgRShdFZJ9NgfPERERSWBk92Bk5+Th0s0UpD/KhY+XO8IDK2JAu1qSfi4DOxERkQQU\nCmdERwWiT+uaeJilQjlPpaQ1dQ0GdiIiIgkpXRXw9/Gw2Oexj52IiEhGGNiJiIhkhIGdiIhIRhjY\niYiIZISBnYiISEYsGthv3ryJqKgobN68GQCQmJiIoUOHIjo6GlOmTEFeXh4AYO/evejTpw/69euH\n77//3pJJJCIismsWC+zZ2dlYvHgxmjdvrt22YsUKREdHY+vWrXjxxRexY8cOZGdnY9WqVfj3v/+N\nTZs24euvv0ZGRoalkklERGTXLBbY3dzcsHbtWvj7+2u3nTt3Dq+++ioAoG3btjhz5gyuXLmCevXq\nwcvLC+7u7mjQoAEuXrxoqWQSEdkUVb4aSenZkj4NjOTFYgvUuLi4wMVF9+NycnLg5uYGAPD19UVy\ncjJSUlJQoUIF7TEVKlRAcnJysef28fGAi4v0q/nYMj8/L2snwSEwny2D+Qyo1QXYsO93nI1LRHJG\nDvzKl0GzkCoY2T0YCkXp62TMY8uwRj7bzMpzgiAYtf156enZ5k6OXfHz80Jy8iNrJ0P2mM+WwXx+\nauvRmzh64a72dVJ6Dvae/AtnDG/aAAAgAElEQVTZOXmIjgos1bmZx5YhZT4XV2Cw6qh4Dw8P5Obm\nAgAePHgAf39/+Pv7IyUlRXtMUlKSTvM9EZHcqfLVuHRTf0vlpZspbJa3EHvtBrFqYI+IiMChQ4cA\nAIcPH0bLli1Rv359XLt2DZmZmXj8+DEuXryIRo0aWTOZREQW9TBLhbRMld596Y9y8TBL/z4yD3VB\nAbYevYm5a89i9pqzmLv2LLYevQl1QYG1kyaKxZri4+LisHTpUiQkJMDFxQWHDh3CJ598glmzZmHb\ntm2oWrUqevXqBVdXV0ybNg2jRo2Ck5MTJkyYAC8v9gURkeMo56lEBW8lUvUEdx8vd5TzVJrlc1T5\naos+dcxebIuN1+kGSc1UaV+XthvEEiwW2ENCQrBp06Yi2zdu3FhkW6dOndCpUydLJIuIyOYoXRUI\nD/TTCS4a4YEVSx2E1eqnNdJLN5ORlqlCBW8lwgP9MKBdLSicHXvdspK6Qfq0rmnzhSCbGTxHRETP\nDGhXC8DTYJL+KBc+Xu4ID6yIXi1rICk9u1S17A37frfrGqmUxHSDWPIRrKZgYCciskEKZ2dERwWi\nT+uaeJilgqeHK3af/C/eW3+uVLVsVb4aZ+MS9e6zlxqplCzVDSIlx25zISKycUpXBfx9PLD75H9x\n9MJdpGaqIOBZLXtbbLxR53uYpUJyRo7efRyY96wbRB9zdINYAgM7EZGNM+f0t3KeSviVL6N3n73U\nSKU2oF0tRDWqDl9vdzg7Ab7e7ohqVF3bPWLr2BRPRGRDVPlqJKdnA05O8CtfBkpXhVn7fZWuCjQL\nqYK9J/8qss9eaqRSK9wNYm+zBhjYiYhsgLqgAN/+dAunryUiN+/pfGl3NwUi61VG71Y1zdrvO7J7\nMLJz8ooMzLNUjdReptlpukHsDQM7EZEN2BYbj9jfEnS25eap8dNvCXBycjLr9DeFwjo1UnVBAbbF\nxnOancQY2ImIrEyVr8bFG0kG91+6mYyFo5r8/7/NV8u2dI3U3hd+sRcM7EREVvYwS4W0R3kG96c9\nUiErO9+u+33lsPCLvWDbBxGRlZXzVKKCl5vB/RW8lNp+dE0t296CINe/txwGdiIiK1O6KtAgyPBT\nLMMD/ewukBemWfhFH0MDAO316WrWxqZ4IiIbMKBdLRQIAk5fu4/cvKeBTDMq3l7mTxfHmPXvOciu\ndBjYiYhsgMLZGUPaB6Ffm1pF5rHLhaH17wsXXDjIrnQY2ImIbIjSVYHq/vJ8VLWYhV84yK702KZB\nREQWVdwAQA6yKz0GdiIishmmDLIjXQzsREQ2yFFHhMvh6WrWxj52IiIbwhHh4gfZkX4M7ERENoQj\nwu3/6WrW5hjFPyIiO2DO567Lgb2usmdtDOxE5LD9ubaGI8LJHNgUT+TA2J9rWzQjws313HVyTPzl\nEjkwTX9uaqYKAp71526Ljbd20hwSR4STOZgc2B8+fGjOdBCRhbE/1zYNaFcLUY2qw9fbHc5OgK+3\nO6IaVeeIcBJNVFP89evXMX/+fGzfvh0AMGXKFBw6dAg+Pj748ssvUb9+fUkTSUTmJ6Y/19/Hw8Kp\nIo4Ip9ISVWN///330bJlSwDA0aNHcfr0aWzatAlvvPEGPv74Y0kTSETS4Apfto0jwslUogL7n3/+\niXHjxgEAfvrpJ3Tu3BmNGzfG66+/jhs3bkiaQCKSBvtzieRJVGB3dXVFfn4+1Go1Tp48ibZt2wIA\nnjx5goKCAkkTSETSYX+uLk77IzkQ1cfeuHFjTJ48GS4uLnByckKLFi2gVquxevVq1K1bV+o0EpFE\n2J/7FKf9kZyIumIXLFiAKlWqQKlUYvXq1XB1dUV2djYOHz6MefPmSZ1GIpKYo/fnctofyYmoGntO\nTg4WLVqks83Lyws//vgjTpw4gcBAx1i/mIjkp6Rpf31a15RNgUeVr8bDLBW8ypWxdlJIQqIC+8CB\nA/Hll18iJCREuy03NxdLlizBnj17cPnyZckSSEQl09ywHbUpvTQcYdpf4a4GP58yCK3py64GmRIV\n2KdNm4ZRo0bhww8/RNu2bXH58mXMmDEDnp6e2LFjh9RpJCID2Ddceo6wjGvhJ8YlpedI8sQ4FjBt\ng6jA3rt3bwQEBGDq1Klo0KABTpw4gVGjRmH8+PFwceFy80TWwkd8lqykYKOZ9vd8PmrIYdqfJboa\nWMC0LaKjcqNGjfDtt99i3Lhx6NKlCyZPnixluoioBI7UN2wKY4KNZnrfpZspSMvMRTlPN4TXriiL\naX+W6GpgAdO2GAzsffr0gZOTU5HtarUau3fvxo0bN+D8/z8ONscTWZ4j9A2XhjHBRuHsjAHtakFd\nIODyzRRkZKlw9XYqFIp4s9U6rdVMLXVXAwuYtsdgYNcsQkNEtkmOfcOqfDUSUx5Dna8uVTAwJdhs\ni43HsYsJ2tfmqnVau5la6q4GFjBtj8HAPnHiRO2/f/31VzRp0sQiCSIiceyxb9hQrVUn+D1SoYJX\n6YKfscFGylqnLTRTP9/VkP4oFxXLPxsVX1pyLGDaO1F97BMmTMCpU6fg5uYmdXqIyAiFb9g+Xu4I\nD7S9vuGSaq3mDn7GBhupap220kxdeIXBmi/54tHDHLOc2x4LmHInKrBPnToVH3zwAaKjo1G1alUo\nFLp/qDJluNgBkTXYy5KwxQXuPq1rmj34GRtspKp12loztWaFQXc3Fzwy43ntpYDpKEQF9qVLl6Kg\noADbtm3Tu//PP/80a6KIyDiaG7YtKqnW2qp+VUmCnzHBRqpap6M0U9tSAZNz6UUG9nXr1kmdDiKS\nqZJqrRCEYoNfGaULktKzjb5RGxtspKh1OloztTULmNYepGhLRAX24gbOzZgxgwPriMigkmqtfj4e\nBoOfh7sLFv37fKlu1GKDjVS1zpIKDKxhmoctDFK0FaICuyAI2LFjB+Li4pCXl6fdnpSUhGvXrkmW\nOCIyji0GCTG11mfB79moeA93V9xJytIea6kbtblrnYYKDOqCAmw9epM1TDOwlUGKtkJUYP/ggw+w\nf/9+hIWF4eeff0bbtm1x/fp1eHt74/PPP5c6jURUAltvhhTbzC0IAgTh6f+TM7L1nstaN+rSFpoK\nFxhYwzQfWxukaG2iAvvBgwexfft2BAQEIDQ0FCtXroRarcbixYtx//59qdNIRCWw9SBRUjN34fSn\nPcrTdxoAlr9RS1FoYg3TvBxlkKJYoq7K7OxsBAQEAAAUCgWePHkChUKByZMnIyYmRtIEElHxSgoS\nqny1hVNkmKbW+nzQKi79+lj6Rq0pdKRmqiDgWaFpW2y8yecUU8Mk8TTdPfrIcZBiSUQF9ho1auC7\n775DQUEBqlWrhsOHDwMAcnJykJGRIWkCiah49h4kiku/Ppa8UUtVaNLUMPVxxBqmOQxoVwtRjarD\n19sdzk6Ar7c7ohpVd8i59KKa4t966y1MnDgR3bp1w+uvv4533nkHMTExSE5Oxquvvip1GomoGPbe\nDFnOUwkfLze9ze9KV2eUdXdFRpbKKoueSNV362jT4CzBlubSW5uowB4REYEzZ85AqVSiX79+qF69\nOq5du4bq1aujY8eOUqeRiIph70FC6apA2TL6A7u/jwfmDG1otRu1VIUmdUEBCgQB7m7OyM0rAAC4\nuykQWa+yQ9YwzcmWF2uyFNHPY1cqn13AzZs3R/PmzSVJEBEZz56X9FTlq5Gdm693n2a7tW7UUhWa\ntsXGI/a3BJ1tuXlqODk52cQsBrJvxQb2YcOGiTrJN998Y5bEEJFp7LkZsvjmbpXVpyqZu9DEEfEk\ntWID+4ULF1ChQgW0atUKDRs2hDNLkmSHbHHRFqnYYzOkrY8RMHehqbiCTGpmLtIyc1HFt6zJ5ycq\nNrCfOHECP/zwA/bu3YuTJ0+iW7du6NWrF4KCgszy4Y8fP8bMmTPx8OFD5OfnY8KECfDz88OCBQsA\nAEFBQVi4cKFZPoscj60v2kJPSdXcbe4CnbkKTcUVZADg6G93MbSDee6x5JiKDex+fn4YPnw4hg8f\njr/++gv79u3DhAkTULZsWfTs2RPdu3eHn5/+uYNi/Oc//8HLL7+MadOm4cGDB3j99dfh5+eHOXPm\nIDQ0FNOmTcOJEyfQunVrkz+DHJetL9pCz5izuduWCnT6ChdKVwVCa/ri2KV7et9zNT4VqrZq2bcu\nkXRED56rUaMGpkyZgilTpuDSpUs4cOAABg4ciJdfftnkp7/5+Pjgxo0bAIDMzEyUL18eCQkJCA0N\nBQC0bdsWZ86cYWAno1m7H9Pem/8tnf7nm7sVbq5Q5+WXamCauQt0xuZHSYWLqEYBBgO7Iy6BSuYl\nOrBrpKWl4dq1a7h27Rry8vJQq5bpo267du2KXbt2oX379sjMzMTq1auxaNEi7X5fX18kJ5e8IpWP\njwdcXOzv5mlOfn5e1k6CTUlMeYy0R4bnHyvcXOFX0fh+zJLyWa0uwIZ9v+NsXCKSM3LgV74MmoVU\nwcjuwVAobL/5397Tn5v3BFdvp+rdd/V2Ksb0KQN3N/G3PVPzY+3ua3oLFx5l3DC6Vz14lSsDf58y\nSErPKfLeiuXLoOZLvkal0xS8Z1iGNfJZ1JWTl5eHo0ePYvfu3Th//jxat26NMWPGoFWrVlAoTA+o\ne/bsQdWqVbF+/Xpcv34dEyZMgJfXs0wQBEHUedLT9T8swlH4+XkhOfmRtZNhU9T5alTwMjwgS52X\nb3SeicnnrUdv6tzQk9JzsPfkX8jOybOL5n9bSH9pruek9Gwk6wmWAJCSkYPbf6caVRM2JT9U+Wqc\nupKgd9+pK/fQuUmAtjle37iC0Jq+ePQwB1L+onnPsAwp87m4AkOxRfBz585hzpw5iIyMxKZNm/Dq\nq6/ixIkTWL58Odq2bVuqoA4AFy9eRIsWLQAAderUgUqlQnp6unb/gwcP4O/vX6rPIMdkjbWj7WnN\ndn3sPf2AeZdqNSY/VPlqJKVna5vsxSzxyyVQSSrF1thff/11VKxYEe3bt0fVqlWRnJysd876xIkT\nTfrwF198EVeuXEHHjh2RkJCAsmXLolq1arhw4QIaNWqEw4cPY+jQoSadm8jSi7bY+6Mj7T39gHlH\n2IvJD99y7kX60kNr+oqavmfPaw/Y+xgSuSs2sPfq1QtOTk4QBAEJCfqblkpjwIABmDNnDoYMGYIn\nT55gwYIF8PPzw/z581FQUID69esjIiLC7J9LjsHSN05bn49dEntPv4a5CnRi8kPfQL1jl+4hwN9T\n7/v0FS7MvfaAlEHXlmYckGHFBvYPP/xQ0g8vW7YsPv/88yLbt27dKunnkmOx1KItcliz3Z7Tr2Gu\nAl1J+QHAYFP945x8tG1QDVfjUy22xK8lgi6nkNoHaYddEjkYe16zHbD/9D/PHAW64vIj9WGuwab6\njCwVOjYOQP+2tSzWZC110LX2FFISj4GdyIyMrS3aWl+lPff7SqG4/BDTVG+p1iJLBF05jMFwFAzs\nRBIo6YZu632V9rjmvJT05YctdV1YIujKZQyGI7D+HYTIAWmaTVMzVRDwrNl0W2y8tZNGRrCVKWvm\nnOZniDWmkJJpDNbYt2zZIvokgwcPNktiiBwB+yrlw1a6LizVeiCnMRhyZjCwr1+/Xud1Wloa8vPz\n4evri4KCAqSlpUGpVCIgIICBncgIcu2rtIXxAtZKgyW7Lgx9R0sEXVspyFDxDAb22NhY7b+//fZb\nxMfHY+rUqdolX9PT07Fs2TLUqVNH+lQSyYjc+iptYbyALaRBaiV9R0sGXY7BsG2irvjVq1djxowZ\nOuu4+/j4YObMmVi9erVkiSOSI7n1VdrCeAFbSIPUxH5HTdBVuip0lrolxyH6ITB3795FzZo1dbbf\nv38feXl5kiSMSM7k0ldpC+MFbCENUjP2OzpCCwYZJiqwd+vWDcOGDUPXrl1RvXp1qNVqJCYm4sCB\nA+jUqZPUaSSSHbn0VdrCeAFbSIMUnu9LN/Y7coU4xyYqsM+ePRu1a9fG0aNHcebMGeTl5cHf3x+v\nv/46hg8fLnESieSrtH2V1h6wZgvjBWwhDeakr7YdWqsifLzckPaoaAtp4e8opnZP8iYqsCsUCgwY\nMAADBgyQOj1EJIKtNLVaY5GWwoUZW1ooxhz0PljmYgIC/D31BvbC31FM7b66+ZNNNkT0ynPbt2/H\nrl27kJSUhNjYWKhUKnz11VcYP358qZ/LTkTGsaWmVkuNFyiuMOMIYxayc/PRNrwqrt5OK/Y7yq0F\ng4wnKrAvX74c+/btw9ChQ/HZZ58BAB4/fozjx48jOzsbM2fOlDSRRPSMrQ0Ws9R4gZIKM/Ifs6BC\nxyYvoH+72sV+R7m1YJDxRLXZ7dy5E1999RWGDx8OJycnAECFChUQExODAwcOSJpAItIlpqm1tEyZ\nJvX8NCtzK6kwo0mnlGmwBDFLw4r5jray1C1Zh6gae3Z2NmrUqFFke4UKFfDw4UOzJ4qIDJOyqdUS\nffemDPiT68j3wsxV25bLrAsyjajAXrt2bezevRu9e/fW2b527VrUqsUSIJElSdnUKmXffWkKDY7U\nb2zO8QJcIc4xiQrsb7/9NsaOHYstW7YgPz8fb775Jm7duoWsrCyuPEdkBVIMFhPbd2/qFLvSFBpK\nW5ix9rRAY7C2TaUlKrA3adIEP/74I/bv34/g4GC4u7ujdevW6N69O7y9vaVOIxEVIsXNv6Tm7rTM\nXBy7lGBSjdscA/5MKczYateCGKxtk6lEBfYVK1Zg8uTJGDVqlM72x48fY9GiRZg/f74kiSOi4pnz\n5l9Sc/fRC3dw7NI97TZjatzm6CM3pTBjq10LRFIq9upLS0vDrVu3sG7dOty+fRvx8fE6/50+fRo7\nduywVFqJSELFPZwmtJYvrt5O1bvv+VHphogZ7W1MOsWMfBc7kt5UjvDgGbJPxdbYT5w4gSVLliA/\nPx9du3bVe0yHDh0kSRgRWZ6h5u624dVw/GKC3veIqXFbY261lCPpbW0tAVPZ09gDEq/YwN67d2/0\n6NEDjRo1wv79+4vsd3d3h6+vr2SJI/vAm4N8GGruVuWrSz0qXWwfeW7eEySlZ5f6epJyJL29T79T\nqwuw9ehNdiPIVIl97AqFApcuXcKDBw+gUChQsWJFAMBff/2lXayGHBP7GOWrcN+9OWrcJfWRa66n\nq7dTkZSeg/KebgivXRHR7QN1riexBUkpWwnsffrdhn2/28ySxGR+ou6+J06cQMeOHXHhwgXttvPn\nz6Nr1644efKkZIkj28Y+RsdirtXMDPWRa66npPQcAEBGVh6OXbqHRf++AHVBAdQFT2uZc9eexew1\nZzF37VlsPXoT6oICydOs7zsYGo9g68u2qvLVOBuXqHefOcYekPWJGhX/6aef4l//+pfOs9cHDBgA\nX19ffPLJJ2jZsqVkCSTbJJc+RhJPyvnVxV1Pd5KysPXoLSicnYyuZYpNsyndSfb64JmHWSokZ+To\n3WcP3QhUMlGB/c6dOzpBXaN169Z45513zJ4osn323sdIppNifvXDLJXeZm2NSzeT4Wyg509MQdJQ\nmkvTnWSvC8mU81TCr3wZbcvI8+yhG4FKJqop/qWXXsKhQ4eKbN+xYweqV+eTfR2ROacvEZXzVKK8\np5vB/Q+z8vQ+ixwo3YNvzNGdZG8PnlG6KtAspIrefbbejUDiiKqxT58+HRMnTsTq1atRrVo1CIKA\n//73v0hKSsLGjRulTiPZID4aksxJ6apAeO2KOgvgPK+CtxKCIOgN7qYWJB25O2lk92Bk5+TZXTcC\niSMqsEdGRuLgwYP48ccfcefOHTg5OSEiIgLdunXjdDcHZq99jGSbotsHIj4hE3eSsors0wxUM2dB\n0pG7kxQK++xGIHFEBXYAqFSpEgYOHIikpCS88MILUqaJbFThAUb22sdItknh7Iz5wxvhP7/8jTNX\nE5HxWIUKegqL5ipI2vuUNXPgevTyJCqwZ2RkYPHixTh48CCcnJwQFxeHtLQ0TJkyBZ9++in8/f2l\nTidZUUkDjHhzIHNRODtjXJ/66N78Rb2FRXMWJNmdRHIlavDcokWLkJWVhe3bt8P5/0eKenh4ICAg\nAO+//76kCSTr43x1eVDlq5GUnm0X85SLG5BmzsFqUs1zJ7ImUTX2kydP4siRIyhfvrx2tTl3d3fM\nmTMHUVFRkiaQrMuRBxjJhaVWCLTHpYXZnURyJCqwu7i4wN3dvcj2vLw8qFSmTTMh++DIA4zkQspH\nlwLyWFqY3UkkJ6J+deHh4Vi6dCkeP36s3fa///0Ps2bNQvPmzSVLHFkf56sbZg9N21I/uhRgVw2R\nrRFVY58/fz7GjRuHJk2aQK1WIywsDCqVCg0bNsSnn34qdRrJijjAqChja6jWbKKWusWFXTVEtkdU\nYK9cuTL+85//4Nq1a7hz5w6USiVefPFF1KrFASaOgPPVdYlt2rZkE7WhwoPUU7rYVUNke0TPY8/L\ny0NmZiZUKhXy8vKQkpKCl156CS4uok9BdooDjJ4xpoYqdd82IG4qopQtLpwLTmR7REXl8+fPY/z4\n8cjJyUH58uUBPJ3b7unpiS+++AINGjSQNJFkGzjASHwN1VJN1GIKD1K2uLCrhsj2iArs7777LoYM\nGYI333wTZcqUAQBkZ2fjq6++wsyZM3HkyBFJE0lkK8TWUC3RRC228CB1iwu7aohsi6jAnpSUhHHj\nxsHN7dnTlzw8PDB+/Hj8+9//liptRDZHbA3VEk3UxhYepGpxkVNXjT3OxScqTFRgb9iwIf7880/U\nr19fZ/utW7fQsGFDSRJGZKvE1FAt0URta/3btthVIzZQy2EuPpGGqMDesmVLTJ06Fa1atcLLL7+M\ngoIC/O9//8PPP/+M1157DVu2bNEeO3jwYMkSS2QLxNZQpW6iZv+2YcYGaksMdCSyFCdBEISSDmrX\nrp24kzk54aeffip1ooyVnPzI4p9pS/z8vBw+DyzB1HyWsnn3WQArWniw15qmOa7nrUdv6i3wRDWq\nXiRQq/LVmLv2rN6WD19vd7w/uqnsCkm8Z1iGlPns5+dlcJ+oGntsbKzZEkPkaKRsopZT/7a5GDsj\ngXPxxeH4A/shqkg/d+5cZGVlFdn+999/Y8iQIWZPFFFh9rB8q6U9nyfmfOKZvRMTqJ/HZZOLpy4o\nwNajNzF37VnMXnMWc9eexdajN6EuKLB20sgAUTX2hIQEdOnSBfPnz0dUVBTUajXWrl2LNWvWoG/f\nvlKnkRyYvQ1qskStxt7yxNKMHVTIsQrF4/gD+yMqsG/cuBGHDx/GkiVLsHv3bty9exdKpRJbtmxB\n3bp1pU4jObDS3lQs1XxoyWC79chNHLt0T/uaN1pdpgRqzsXXj88CsE+i14Pt0KED0tPTsXDhQpQp\nUwYrV65kUCdJleamYularaWWj9169BZOXL6ndz9vtM8YG6g5VkE/jj+wT6IC+/Xr17Fw4UJkZWXh\nu+++w507dzB9+nRERERg9uzZqFChgtTpJAdk6k1Fla/G5kM3cCruvnablLVaSy4fe+xigsH9tnyj\ntfTAK1MDtS3OxbcmW1srgcQRVXUZMGAAIiMjsWvXLoSGhqJr16744Ycf4OzsjE6dOkmdRnJQxg5q\n0gzyeferMzpB/Xnmegb584wdrGWK4goPGrZ4o7X2wCsOKiwdTbeGPhx/YLtE1dh37txZ5BGt5cuX\nx9KlS3Hq1ClJEkZkbF9p4eZwfaSo1Vp7+VgNW7zRcuCV/eP4A/tTbGDftm0bBgwYoA3qgiDAycmp\nyDGRkZHSpZAcmtibipgaLSBNrdbay8c6OwGtw6ra3I2WA6/kgeMP7E+xgf2DDz7AgAEDtK/DwsJw\n5coVnWNOnDhRqgTs3bsX69atg4uLCyZPnoygoCDMmDEDarUafn5++Pjjj3UePkOORexNRUyNFpCu\nVmvN5WNbh1fD0A5BZvkcc+LAK3nh+AP7UWxgL7zarL7VZ0WsSGtQeno6Vq1ahZ07dyI7OxsxMTE4\ndOgQoqOj0blzZ3z22WfYsWMHoqOjTf4MkoeSbirF1WgBwPe5UfHFMXWQl6YA0j3iJdxNykJ1f094\neZi3QGpvTaKmdlHk5j1BUno2a4ZEJio2sBdudi/82tA2sc6cOYPmzZvD09MTnp6eWLx4Mdq1a4eF\nCxcCANq2bYsNGzYwsFOJiqvRRoRUxtCOQZI+3csS0+vsrUnU2C4KTR5evZ2K5PQcLrxDZCLR89il\ncPfuXeTm5mLs2LHIzMzEpEmTkJOTo2169/X1RXKyiH5THw+4uNjuDc4SinsggKOY2D8cHmXccDYu\nESkZOahYvgyahVTByO7BUCiKDwxrd1/TO8jLo4wbRveqp91uKJ/Fvt9YuXlPkJ6pgo+3Eu5uz36u\n1U0+o2UZ8zeRKg9JP94zLMMa+WzVwA4AGRkZWLlyJe7du4dhw4bpNO2LbeZPT8+WKnl2gU9qeqZX\n5Evo3CRAp0ablva42Peo8tU4dUX//PBTV+6hc5MAKF0VBvNZ7PuNIadlY8X8TaTIQzKM9wzLsMmn\nu6nVamzdulUbYAu/1mwzla+vL8LDw+Hi4oIXXngBZcuWhUKhQG5uLtzd3fHgwQP4+/ubfH5yTMYO\n8intIC8pBonJbZpYSX8TDrQjMp9iA7u/vz/WrVtn8LVmm6latGiBWbNmYfTo0Xj48CGys7PRokUL\nHDp0CD179sThw4fRsmVLk89PJEZp56Gbex67Kl+NizeS9O6T6zQxrnBGZD7FBnapn8NeqVIldOzY\nEf379wfw9PGw9erVw8yZM7Ft2zZUrVoVvXr1kjQNRKWdh27OeezqggJsPnQDaY/y9O63hdqrFMvD\n8glrROZj9T72gQMHYuDAgTrbNm7caKXUkCN5PkCVdiqZuaaibYuNN7gcLmDd2qvU/f6avLp6OxUp\nGTk2P52PyFZZPbATWVpxAcrUqWTmmIomZvU8a9Zepe731+ThmD5lcPvvVJufzkdkq+xreC2RGWgC\nVGqmCgKeBahtsfGlfgIi25cAABLiSURBVGhIad5f0up5ESGVrVZ7LWl5WHM+WMfdzYUPbiEqBQZ2\nciiWDFDGKu5pdr7eSgztGGS1qW6WeIIdEZkHAztJRpWvRlJ6tlWDZWG2HKCKf0Smn1VrsMY+QpeI\nrId97GR2try4iq1Pq7LV9eA5ap3IfjCwk9lZYnEVU6dc2XqAkmo9eHNMUbPVQgcR6WJgJ7OS+hnc\n5mgNsIcAZa5HZJqz9cTeHkJD5KgY2MmspF4a1BytAY4UoKRoPeFzuYlsGwfPkVlJOcjK3CPajZ2a\npnlOuC0NBiyOLc8AICLpsMZOZiVlH7a1HhRir88J54NViBwTA3shUqyD7Wik6sO21oh2e33Smq3P\nACAiaTCw/z9bnqJlb6Tqw7bGiHapBwNKydZnABCRNBjY/5+91spsSeHWDmMHWYlpLbH0iHZ7b862\nhxkARGReDOyw71qZLShta4cx77f0iHZ7as7WVzBypBkARPQUAzvsv1ZmbaVt7TDl/ZaacmUPzdli\nCkacokbkONh5DK6DXRqlnVJlD1OyBrSrhahG1eHvUwbOToCvtzuiGlW3mebs4p5WR0SOhzV22Eet\nzFaVtrXDHlpLbPk54exGIqLCWGP/f5pama+3u03WymxVaVs77Km1xJTnhEv9hDtbflodEVkHa+z/\nj4OMTFPa1g65tpZYavqkPQ3uIyLLYGAvhIOMiqdv5HVpp1TJcUqWpaZPyrVgRESmY2B3UMausFdS\nDbQ0rR1yay2xdL+3HAtGRGQ6BnYHY2oTsZgaaGlbO+TSWmLpAYFyKxgRUelw8JyDMWVqlD1MSbMl\n1hoQaOzT6ohInhjYHYipAZojr42j6ffWh/3eRCQ1NsU7EFObiDny2njs9yYia2FgdyCmBmiOvDae\nrfZ787HERPLHwO5AShOgWQM1ja0MCORjiYkcBwO7gzE1QNtqDZTE4WOJiRwHA7uDKW2AtpUaKInH\n9eSJHAvb4BwUp0Y5Ds5qIHIsDOxEMmdPD9ohotJjYCeSOc6rJ3Is7GMncgCc1UDkOBjYiRwAZzUQ\nOQ4GdiIHwlkNRPLHPnYqlipfjaT0bD7ohYjITrDGTnpxpTIiIvvEOzTpZcrjXe2RoRYJtlQQkb1i\njZ2KcISVygy1SPRtUwM7jv+lt6WCiMgeMLBTEaY+3tWeGFo7/cb/MnAnKavIdgCYMqihxdNJRGQs\nNsVTEXJfqay4FomE5Cy92y/dTEFu3hMpk0VEZBYM7FSE3FcqK65FokDQ/570R7lIN/AeIiJbwqZ4\n0kvOK5VpWiRS9QRqZyf9wd3Hyx0+3ko8ephjgRQSEZmOgZ30kvNKZZoWief72DWq+Xnq9LFrhAdW\nhLubCx5ZIoFERKXAwE7FkutKZYZaJJ6NipdfSwUROQYnQRAM9Craj+Rkx65H+fl5OXwemEqVr9bb\nIqFvO/PZMpjP0mMeW4aU+ezn52VwH2vs5NAMtUjItaWCiOSPo+KJiIhkhIGdbAKXcCUiMg82xZNV\n8WEzRETmxcBOVmVoaVcAiI4KtFayiIjsFqtEZDUlPWyGzfJERMZjYCerEfOwGSIiMo5NBPbc3FxE\nRUVh165dSExMxNChQxEdHY0pU6YgLy/P2skjicj9YTNERNZgE4F99erVKFeuHABgxYoViI6Oxtat\nW/Hiiy9ix44dVk4dSUXuD5shIrIGqwf227dvIz4+Hm3atAEAnDt3Dq+++ioAoG3btjhz5owVU0dS\nG9CuFqIaVYevtzucnQBfb3dENarOJVyJiExk9VHxS5cuxbx587B7924AQE5ODtzc3AAAvr6+SE7W\nP7jqeT4+HnBxcezaXXHLC9q6KYMaIjfvCdIzVfDxVsLdzeqXpUH2nM/2hPksPeaxZVgjn616B929\nezfCwsIQEBCgd7/YZezT07PNmSy7I5d1n10APHqYY7NPUJNLPts65rP0mMeW4ZBrxR8/fhx37tzB\n8ePHcf/+fbi5ucHDwwO5ublwd3fHgwcP4O/vb80kEhER2RWrBvbly5dr/x0TE4Nq1arh0qVLOHTo\nEHr27InDhw+jZcuWVkwhERGRfbH64LnCJk2ahN27dyM6OhoZGRno1auXtZNERERkN2xmlNKkSZO0\n/964caMVU0JERGS/bK7GTkRERKZjYCciIpIRBnYiIiIZYWAnIiKSEQZ2IiIiGWFgJyIikhEGdiIi\nIhlhYCciIpIRBnYiIiIZYWAnIiKSEQZ2IiIiGWFgJyIikhEGdiIiIhlhYCciIpIRBnYiIiIZYWAn\nIiKSEQZ2MkiVr0ZSejZU+WprJ4WIiERysXYCyPaoCwqwLTYel24mIy1ThQreSoQH+mFAu1pQOLMs\nSERkyxjYqYhtsfE4euGu9nVqpkr7Ojoq0FrJIiIiEVj9Ih2qfDUu3UzWu+/SzRQ2yxMR2TgGdtLx\nMEuFtEyV3n3pj3LxMEv/PiIisg0M7KSjnKcSFbyVevf5eLmjnKf+fUREZBsY2EmH0lWB8EA/vfvC\nAytC6aqwcIqIiMgYHDxHRQxoVwvA0z719Ee58PFyR3hgRe12IiKyXQzsVITC2RnRUYHo07omHmap\nUM5TyZo6EZGdYGAng5SuCvj7eFg7GUREZAT2sRMREckIAzsREZGMMLATERHJCAM7ERGRjDCwExER\nyQgDOxERkYwwsBMREckIAzsREZGMOAmCIFg7EURERGQerLETERHJCAM7ERGRjDCwExERyQgDOxER\nkYwwsBMREckIAzsREZGMMLATERHJiIu1E0DGycnJwaxZs5CamgqVSoXx48ejTp06mDFjBtRqNfz8\n/PDxxx/Dzc3N2km1e7m5uejWrRvGjx+P5s2bM4/N7Ny5c5gyZQpq164NAAgMDMQbb7zBfJbA3r17\nsW7dOri4uGDy5MkICgpiPpvZ999/j71792pfx8XF4dtvv8WCBQsAAEFBQVi4cKFF0sIFauzMgQMH\nkJCQgNGjRyMhIQEjR45EgwYN0KpVK3Tu3BmfffYZKleujOjoaGsn1e4tW7YMv/zyCwYPHozz588z\nj83s3Llz2LJlC1asWKHdNnv2bOazmaWnp2PgwIHYuXMnsrOzERMTgydPnjCfJfTrr7/ixx9/RHx8\nPN555x2EhoZi2rRp6NGjB1q3bi3557Mp3s506dIFo0ePBgAkJiaiUqVKOHfuHF599VUAQNu2bXHm\nzBlrJlEWbt++jfj4eLRp0wYAmMcWwnw2vzNnzqB58+bw9PSEv78/Fi9ezHyW2KpVq7SVr9DQUACW\nzWcGdjs1cOBATJ8+HXPmzEFOTo62Gc3X1xfJyclWTp39W7p0KWbNmqV9zTyWRnx8PMaOHYtBgwbh\n1KlTzGcJ3L17F7m5uRg7diyio6Nx5swZ5rOErl69iipVqkChUMDb21u73ZL5zD52O/Xdd9/hzz//\nxDvvvIPne1PYs1J6u3fvRlhYGAICAvTuZx6bx0svvYSJEyeic+fOuHPnDoYNGwa1Wq3dz3w2n4yM\nDKxcuRL37t3DsGHDeM+Q0I4dO9C7d+8i2y2ZzwzsdiYuLg6+vr6oUqUKXnnlFajVapQtWxa5ublw\nd3fHgwcP4O/vb+1k2rXjx4/jzp07OH78OO7fvw83Nzd4eHgwj82sUqVK6NKlCwDghRdeQMWKFXHt\n2jXms5n5+voiPDwcLi4ueOGFF1C2bFkoFArms0TOnTuHuXPnwsnJCRkZGdrtlsxnNsXbmQsXLmDD\nhg0AgJSUFGRnZyMiIgKHDh0CABw+fBgtW7a0ZhLt3vLly7Fz505s374d/fr1w/jx45nHEti7dy/W\nr18PAEhOTkZqaipee+015rOZtWjRAmfPnkVBQQHS09N5z5DQgwcPULZsWbi5ucHV1RU1atTAhQsX\nAFg2nzkq3s7k5ubi3XffRWJiInJzczFx4kSEhIRg5syZUKlUqFq1KpYsWQJXV1drJ1UWYmJiUK1a\nNbRo0YJ5bGZZWVmYPn06MjMzkZ+fj4kTJ+KVV15hPkvgu+++w44dOwAA48aNQ7169ZjPEoiLi8Py\n5cuxbt06AE/HkMyfPx8FBQWoX78+Zs+ebZF0MLATERHJCJviiYiIZISBnYiISEYY2ImIiGSEgZ2I\n6P/au9uQptowDuD/zZdpm2kmYbgkSQyKtRyYI9DSnI2ojhKG9qFIS9RKwmwmlH0wSqZRSQvTDxH2\nKlmrrFyLMOxLImnNSMRet9WM8mXzZC7nng/S4Vlq+cRTtnH9YLD7vs99X9cO4sW52c4hxINQYSeE\nEEI8CBV2Qsj/pru7G0qlElKpFIODg9OSw9WrVxEbGzstsQn5G1BhJ+QvkZiYiHPnzo3rd6dCVVdX\nhxkzZqC1tRUikWjcOMuyKCsrQ1JSEqRSKaKjo7F161a0tbVxx5hMJty+fftPpk2IR6HCTgj539hs\nNojF4klvdrJ37148e/YMNTU1aGtrQ1NTExYvXozMzEx8+PABwNgduhobG/9k2oR4FCrshLiZnp4e\n7Ny5E3K5HDKZDLm5ubBYLADG7lO9cOFCsCzLHb9v3z7k5+cDGLv6VyqVqKioQHR0NIxGI548eYL0\n9HTIZDIsW7YMu3fvhtVqnTC23W5HWVkZEhISsGTJEqSlpXG3zFSpVNBqtdDr9ZBIJLDZbOPmP3z4\nEBs3bkRERAT4fD4CAwNRUFCAgwcPgs/no7q6GuXl5dwadrt93E7G95/x6dOnYBgGS5cuxZYtW1ye\noJWcnIwzZ8645HDo0CFkZ2f/yqknxC1QYSfEzezYsQM+Pj7Q6/W4f/8+RkZGsGfPninP//jxI3g8\nHlpaWiAWi6FSqbB8+XK0tLRAr9eDZVlUVVVNOPfYsWNobm7G2bNn0drairi4OOTk5GBgYABqtRoM\nw0ChUMBgMCAgIGDc/MjISJw/fx6vXr3i+vh8PlJSUhASEoLs7GyXNb49WnQyDocD+fn5kMvlePTo\nEQoLC3Hp0iVunGEY3Lhxg2s7nU7o9XqsX79+yueLEHdDhZ2Qv8iRI0cgkUhcXgcOHODGOzs7YTAY\nUFRUhICAAAQFBWHXrl1obW3ltrJ/ZnBwENu3b4ePjw94PB6sViv8/Pzg7e2NwMBAnD59GiqVasK5\nV65cQXZ2NsLDw+Hr64u8vDyMjo6iubl5SrHLysrAsiyUSiUUCgWKi4tx584dfP36dUrzv9fR0QGL\nxYLc3FwIBAJIJBIolUpunGEYPH/+HC9evAAwdnVvs9mwatWqX4pHiDugwk7IX6S4uBgGg8HlVVpa\nyo0bjUYIhUKEhoZyfeHh4QAAs9k8pRgikQgzZ87k2gUFBdBoNFizZg0OHz6Mjo6OCecNDAzAarUi\nMjKS6/P29kZYWNiUY0dFReHmzZu4du0aMjIy0NfXh6KiIjAMg97e3imt8W8WiwUikQhBQUFcX0RE\nBPdeLBYjJiYG169fBwDodDokJyfD39//P8cixF1QYSfEjdjt9knHeDzehP0Oh8Ol7eXl5dJOS0tD\nU1MTsrKyYDKZkJ6ePuG3838l9mQWLVqEzMxMVFVVQafTob+/HxcuXJjS3NHRUZecvv98/x4HgNTU\nVDQ0NMDpdOLu3bu0DU88HhV2QtzIvHnzwLIsenp6uL6XL1+Cx+MhPDwcAoEAwNjjfb8xGo0/XLO3\ntxezZs3Chg0bcOrUKeTl5eHy5cvjjps9ezaEQiG3rQ0Aw8PDMJvN3K7Bj3R1daG0tHRcIZ47dy4W\nLFgw6e/efX19MTQ0xLXfvn3LvZ8zZw4+f/6M/v5+rq+7u9tl/urVq9HX14e6ujoMDw9DLpf/NFdC\n3BkVdkLciEQiQVRUFNRqNViWxadPn1BZWYkVK1YgODgYYrEYXl5eaGxsxMjICG7duoU3b95Mup7F\nYkF8fDz0ej0cDgcGBwfR1dU1YaHm8/lgGAY1NTUwm8348uULKisr4e/vj7i4uJ/mHhISgoaGBuzf\nvx8mkwlOpxMsy6K+vh7t7e1ISEgAAAgEArx79w5WqxUjIyOYP38+Hjx4gKGhIRiNRmi1Wm5NqVSK\noKAgVFdXw263o729Hffu3XOJKxQKoVAoUF5ejrVr14LPp397xLPRXzghboTH40Gj0WBgYACJiYlI\nSUlBWFgYKioqAIwVz8LCQpw8eRKxsbF4/PgxGIaZdL3Q0FCo1WqcOHECMpkMSUlJAICSkpIJj1ep\nVJBKpcjIyEB8fDw6OztRW1sLoVD409yDg4Nx8eJF2O12bNq0CVKpFHFxcdBqtdBoNNxNeNatWweT\nyYSVK1fi/fv33M/v5HI5CgoKsG3bNm5NPz8/aDQaNDc3IyYmBkePHkVWVta42KmpqbDZbD88F4R4\nCp7T6XROdxKEEPI7abVa1NbWor6+frpTIeS3oyt2QohHe/36NY4fP46cnJzpToWQP8J7uhMghJDf\npaSkBDqdDps3b4ZCoZjudAj5I2grnhBCCPEgtBVPCCGEeBAq7IQQQogHocJOCCGEeBAq7IQQQogH\nocJOCCGEeJB/APWJGrHXQa7lAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f291afff048>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "Yrjucdifq_mt",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Hyperparameters"
      ]
    },
    {
      "metadata": {
        "id": "OwVfkk3RrC_I",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "learning_rate = 0.0001\n",
        "max_iteration = 50"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "EzXaG70OrZtn",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Parameters"
      ]
    },
    {
      "metadata": {
        "id": "2INJM9AIrcBu",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "m = 0\n",
        "b = 0"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "FPt2eKjBr1Lx",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Hypothesis"
      ]
    },
    {
      "metadata": {
        "id": "enVE4tHWsBBF",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def h (m, b, X) :\n",
        "  return m * X + b"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "IA9I6vaXs7nb",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Loss Function"
      ]
    },
    {
      "metadata": {
        "id": "3KOQVUjBs-Ub",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def loss (m, b, X, Y) :\n",
        "  return np.average(np.square(Y - h(m, b, X))) / 2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "7TE79NG-tyLG",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Calculate Gradients"
      ]
    },
    {
      "metadata": {
        "id": "yy9yxye4t0BJ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def gradient (m, b, X, Y) :\n",
        "  dm = - np.average((Y - h(m, b, X)) * X)\n",
        "  db = - np.average(Y - h(m, b, X))\n",
        "  return (dm, db)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "jVo5TbKyu9KL",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Gradient Descent"
      ]
    },
    {
      "metadata": {
        "id": "fprg4-tcu-4v",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def gradient_descent (m, b, X, Y, learning_rate, max_iteration) :\n",
        "  for i in range(max_iteration) :\n",
        "    dm, db = gradient (m, b, X, Y)\n",
        "    m -= learning_rate * dm\n",
        "    b -= learning_rate * db\n",
        "    if i % 10 == 0 :\n",
        "      print ('iteration : ', i, ' loss : ', loss(m, b, X, Y)) \n",
        "  return (m, b)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "uMIZFxUhwQZO",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Train Model"
      ]
    },
    {
      "metadata": {
        "id": "-0okDGSCwUC7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "221dd109-c839-49b7-e354-29ab97c6fa8b"
      },
      "cell_type": "code",
      "source": [
        "m, b = gradient_descent (m, b, X, Y, learning_rate, max_iteration)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration :  0  loss :  1593.1334591670338\n",
            "iteration :  10  loss :  61.30482288585254\n",
            "iteration :  20  loss :  56.34127863702311\n",
            "iteration :  30  loss :  56.32510567688097\n",
            "iteration :  40  loss :  56.324963270541446\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "MFp2MUlexVd5",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Optimal values of Parameters using Trained Model"
      ]
    },
    {
      "metadata": {
        "id": "tcMQWkuvwYu7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "02ba6dd8-b680-4582-e5ad-95a81c741121"
      },
      "cell_type": "code",
      "source": [
        "m, b"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1.4788903781318357, 0.030569950649287976)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "metadata": {
        "id": "vsa_VlHd8ged",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Linear Regression using *polyfit*  function of **numpy**"
      ]
    },
    {
      "metadata": {
        "id": "WJajnpzW8p2L",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "np_m, np_b = np.polyfit(X, Y, 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "MjJ7Di8z8-Qb",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Optimal values of Parameters using Numpy Linear Regression"
      ]
    },
    {
      "metadata": {
        "id": "z4G5h9Ki7IJi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "03017381-1e77-448b-e667-720a070833f7"
      },
      "cell_type": "code",
      "source": [
        "np_m, np_b"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1.32243102275536, 7.991020982270385)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "metadata": {
        "id": "Dh6PmQOwxcKk",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Visualize the Data"
      ]
    },
    {
      "metadata": {
        "id": "B0h7MJE0xcKo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 404
        },
        "outputId": "5218e8ce-c82d-47cd-9631-29c1fd90a2e3"
      },
      "cell_type": "code",
      "source": [
        "fig = plt.figure()\n",
        "\n",
        "# Generate data for plotting Line\n",
        "x = np.arange(25, 75)\n",
        "y = [m * x_i + b for x_i in x]\n",
        "\n",
        "# Generate data for plotting Line Numpy Linear Regression\n",
        "np_x = np.arange(25, 75)\n",
        "np_y = [np_m * x_i + np_b for x_i in np_x]\n",
        "\n",
        "# plot data and best-fit lines\n",
        "plt.plot(X, Y, 'o', x, y, '-', np_x, np_y, '--')\n",
        "plt.legend(loc='upper left', labels=['data points', 'best-fit line', 'numpy line'])\n",
        "\n",
        "fig.suptitle('Linear Regression : Expected Marks vs Hours of Study', fontsize=18)\n",
        "plt.xlabel('Hours of Study', fontsize=14)\n",
        "plt.ylabel('Expected Marks', fontsize=14)\n",
        "plt.show()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gSFsWnPLUlsW+8lx6ejqTJk2iZcuW+Pr6smPHDoPXdTrdc+soiBWFgi+FE3Qi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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f291ab47048>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}